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'''Matching''' is a statistical technique which is used to evaluate the effect of a treatment by comparing the treated and the non-treated units in an [[observational study]] or [[quasi-experiment]] (i.e. when the treatment is not randomly assigned). The goal of matching is, for every treated unit, to find one (or more) non-treated unit(s) with similar observable characteristics against whom the effect of the treatment can be assessed. By matching treated units to similar non-treated units, matching enables a comparison of outcomes among treated and non-treated units to estimate the effect of the treatment reducing bias due to [[confounding]].<ref>{{cite journal | doi=10.2307/2529684 | last=Rubin | first=Donald B. | title=Matching to Remove Bias in Observational Studies | journal=Biometrics | volume=29 | issue=1 | year=1973 | pages=159–183 | jstor=2529684}}</ref><ref>{{cite journal | title=On Stratification, Grouping and Matching | last=Anderson | first=Dallas W. |author2=Kish, Leslie |author3=Cornell, Richard G. | journal=Scandinavian Journal of Statistics | volume=7 | issue=2 | year=1980 | pages=61–66 | jstor=4615774}}</ref><ref>{{cite journal | doi=10.2307/2530417 | title=Matching in Epidemiologic Studies: Validity and Efficiency Considerations | last=Kupper | first=Lawrence L. |author2=Karon, John M. |author3=Kleinbaum, David G. |author4=Morgenstern, Hal |author5= Lewis, Donald K. | journal=Biometrics | volume=37 | issue=2 | year=1981 | pages=271–291 | jstor=2530417 | pmid=7272415| citeseerx=10.1.1.154.1197 }}</ref> [[Propensity score matching]], an early matching technique, was developed as part of the [[Rubin causal model]],<ref name="Rosenbaum Rubin">{{cite journal |last1=Rosenbaum |first1=Paul R. |last2=Rubin |first2=Donald B. |title=The Central Role of the Propensity Score in Observational Studies for Causal Effects |journal=[[Biometrika]] |year=1983 |volume=70 |issue=1 |pages=41–55 |doi=10.1093/biomet/70.1.41 |doi-access=free }}</ref> but has been shown to increase model dependence, bias, inefficiency, and power and is no longer recommended compared to other matching methods.<ref>{{Cite journal|last1=King|first1=Gary|last2=Nielsen|first2=Richard|date=October 2019|title=Why Propensity Scores Should Not Be Used for Matching|url=https://www.cambridge.org/core/product/identifier/S1047198719000111/type/journal_article|journal=Political Analysis|language=en|volume=27|issue=4|pages=435–454|doi=10.1017/pan.2019.11|issn=1047-1987|doi-access=free}}</ref>

Matching is a statistical technique which is used to evaluate the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned). The goal of matching is, for every treated unit, to find one (or more) non-treated unit(s) with similar observable characteristics against whom the effect of the treatment can be assessed. By matching treated units to similar non-treated units, matching enables a comparison of outcomes among treated and non-treated units to estimate the effect of the treatment reducing bias due to confounding. Propensity score matching, an early matching technique, was developed as part of the Rubin causal model, but has been shown to increase model dependence, bias, inefficiency, and power and is no longer recommended compared to other matching methods.

匹配是一种统计方法，在观察研究或准实验研究（即）内经处理及未经处理的单位，以评估处理的效果。。匹配的目标是，对于每个治疗单位，找到一个(或多个)非治疗单位具有类似的可观察特征，对照治疗的效果可以进行评估。通过将治疗单位与类似的非治疗单位进行匹配，匹配可以使治疗单位与非治疗单位之间的结果进行比较，从而评估治疗减少混杂造成的偏倚的效果。早期的匹配技术---- 倾向评分匹配匹配技术，是作为虚拟事实模型匹配技术的一部分而发展起来的，但已经被证明会增加模型依赖性、偏倚、低效和功率，与其他匹配方法相比不再被推荐使用。

Matching has been promoted by [[Donald Rubin]].<ref name="Rosenbaum Rubin" /> It was prominently criticized in [[economics]] by LaLonde (1986),<ref>

Matching has been promoted by Donald Rubin. who compared estimates of treatment effects from an experiment to comparable estimates produced with matching methods and showed that matching methods are biased. Dehejia and Wahba (1999) reevaluated LaLonde's critique and showed that matching is a good solution. Similar critiques have been raised in political science and sociology journals.

配对活动由唐纳德•鲁宾(Donald Rubin)推动。他们将实验中的治疗效果评估与匹配方法产生的可比评估进行了比较，并表明匹配方法是有偏差的。德赫加和瓦巴(1999)重新评价了拉隆德的批评，并指出匹配是一个很好的解决方案。类似的批评在政治学和社会学期刊上也被提出。

{{cite journal | last = LaLonde | first = Robert J. | title = Evaluating the Econometric Evaluations of Training Programs with Experimental Data | journal = [[American Economic Review]] | volume = 76 | issue = 4 |year = 1986 | pages = 604–620 | jstor=1806062 }}</ref> who compared estimates of treatment effects from an [[experiment]] to comparable estimates produced with matching methods and showed that matching methods are [[Bias (statistics)|biased]]. Dehejia and Wahba (1999) reevaluated LaLonde's critique and showed that matching is a good solution.<ref>

{{cite journal | title = Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs |

first1 = R. H. |last1=Dehejia |first2 = S. |last2=Wahba |journal=[[Journal of the American Statistical Association]] |year=1999 |volume=94 |issue=448 |pages=1053–1062 |doi=10.1080/01621459.1999.10473858 |

url = http://www.nber.org/papers/w6586.pdf }}</ref> Similar critiques have been raised in [[political science]]<ref>{{cite journal |last1=Arceneaux |first1=Kevin |first2=Alan S. |last2=Gerber |first3=Donald P. |last3=Green |year=2006 |title=Comparing Experimental and Matching Methods Using a Large-Scale Field Experiment on Voter Mobilization |journal=Political Analysis |volume=14 |issue=1 |pages=37–62 |doi=10.1093/pan/mpj001 }}</ref> and [[sociology]]<ref>{{cite journal |last1=Arceneaux |first1=Kevin |first2=Alan S. |last2=Gerber |first3=Donald P. |last3=Green |year=2010 |title=A Cautionary Note on the Use of Matching to Estimate Causal Effects: An Empirical Example Comparing Matching Estimates to an Experimental Benchmark |journal=Sociological Methods & Research |volume=39 |issue=2 |pages=256–282 |doi=10.1177/0049124110378098 |s2cid=37012563 }}</ref> journals.

When the outcome of interest is binary, the most general tool for the analysis of matched data is conditional logistic regression as it handles strata of arbitrary size and continuous or binary treatments (predictors) and can control for covariates. In particular cases, simpler tests like paired difference test, McNemar test and Cochran-Mantel-Haenszel test are available.

当感兴趣的结果是二进制的时候，分析匹配数据最常用的工具是条件 Logit模型，因为它可以处理任意大小的层次和连续或二进制处理(谓词) ，并且可以控制协变量。在特定情况下，可以使用配对差异检验、 McNemar 检验和 cochran-mantel-haenzel 检验等更简单的检验。

== Analysis ==

When the outcome of interest is continuous, estimation of the average treatment effect is performed.

当感兴趣的结果是连续的，估计的平均治疗效果进行。

When the outcome of interest is binary, the most general tool for the analysis of matched data is [[conditional logistic regression]] as it handles strata of arbitrary size and continuous or binary treatments (predictors) and can control for covariates. In particular cases, simpler tests like [[paired difference test]], [[McNemar test]] and [[Cochran-Mantel-Haenszel test]] are available.

Matching can also be used to "pre-process" a sample before analysis via another technique, such as regression analysis.

匹配也可以用于“预处理”样品，然后再通过另一种技术进行分析，例如回归分析分析。

When the outcome of interest is continuous, estimation of the [[average treatment effect]] is performed.

Matching can also be used to "pre-process" a sample before analysis via another technique, such as [[regression analysis]].<ref>{{cite journal |last1=Ho |first1=Daniel E. |first2=Kosuke |last2=Imai |first3=Gary |last3=King |first4=Elizabeth A. |last4=Stuart |author4-link= Elizabeth A. Stuart |year=2007 |title=Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference |journal=Political Analysis |volume=15 |issue=3 |pages=199–236 |doi=10.1093/pan/mpl013 |doi-access=free }}</ref>

Overmatching is matching for an apparent mediator that actually is a result of the exposure. If the mediator itself is stratified, an obscured relation of the exposure to the disease would highly be likely to be induced.

过匹配是匹配的一个明显的中介，实际上是一个结果的曝光。如果中介者本身是分层的，则很可能诱发一种模糊的疾病暴露关系。

== Overmatching ==

For example, matching the control group by gestation length and/or the number of multiple births when estimating perinatal mortality and birthweight after in vitro fertilization (IVF) is overmatching, since IVF itself increases the risk of premature birth and multiple birth.

例如，在估算新生儿死亡和体外受精后出生体重时，按妊娠期长度和/或多胎次数与对照组相匹配是过度匹配的，因为体外受精本身会增加早产和多胎的风险。

''Overmatching'' is matching for an apparent mediator that actually is a result of the exposure. If the mediator itself is stratified, an obscured relation of the exposure to the disease would highly be likely to be induced.<ref name=marsh/> Overmatching thus causes [[statistical bias]].<ref name=marsh>{{cite journal |title=Removal of radiation dose response effects: an example of over-matching |last1=Marsh |first1=J. L. |last2=Hutton |first2=J. L. | author2-link = Jane Hutton |last3=Binks |first3=K. |year=2002 |journal=[[British Medical Journal]] |volume=325 |issue=7359 |pages=327–330 |pmid=12169512 |doi=10.1136/bmj.325.7359.327 |pmc=1123834}}</ref>

It may be regarded as a sampling bias in decreasing the external validity of a study, because the controls become more similar to the cases in regard to exposure than the general population.

它可以被看作是一个减少研究外部效度的抽样偏差，因为在暴露方面，控制变得比一般人群更加类似于案例。

For example, matching the control group by gestation length and/or the number of [[multiple birth]]s when estimating [[perinatal mortality]] and birthweight after [[in vitro fertilization]] (IVF) is overmatching, since IVF itself increases the risk of premature birth and multiple birth.<ref>{{cite journal |title=The danger of overmatching in studies of the perinatal mortality and birthweight of infants born after assisted conception |last1=Gissler |first1=M. |last2=Hemminki |first2=E. |journal=Eur J Obstet Gynecol Reprod Biol |year=1996 |volume=69 |issue=2 |pages=73–75 |pmid=8902436 |doi=10.1016/0301-2115(95)02517-0}}</ref>

It may be regarded as a [[sampling bias]] in decreasing the [[external validity]] of a study, because the controls become more similar to the cases in regard to exposure than the general population.

== See also ==

{{Portal|Mathematics|Medicine}}

* [[Propensity score matching]]

== References ==

{{reflist|30em}}

== Further reading ==

*{{cite book |last1=Angrist |first1=Joshua D. |last2=Pischke |first2=Jörn-Steffen |chapter=Regression Meets Matching |title=Mostly Harmless Econometrics: An Empiricist's Companion |publisher=Princeton University Press |year=2009 |isbn=978-0-691-12034-8 |pages=69–80 }}

{{Statistics}}

Category:Bias

类别: 偏见

Category:Design of experiments

类别: 实验设计

{{Authority control}}

Category:Medical statistics

类别: 医学统计

Category:Observational study

类别: 观察性研究

[[Category:Bias]]

Category:Sampling techniques

类别: 抽样技术

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This page was moved from [[wikipedia:en:Matching (statistics)]]. Its edit history can be viewed at [[匹配/edithistory]]</noinclude>

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